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Real tree

In mathematics, real trees (also called R {\displaystyle \mathbb {R} } -trees) are a class of metric spaces generalising simplicial trees. They arise naturally in many mathematical contexts, in particular geometric group theory and probability theory. They are also the simplest examples of Gromov hyperbolic spaces.

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Overview

Definition and examples

Characterizations

Examples

Generalisations

Advanced semantic analysis

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Map overview Semantic statistics

Real tree

Nodes45
Edges44
Triples37
Avg. degree1.96
Density0.044444
Components1

How this topic connects Entity context

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Real tree

Top relations

related to Simple examples · 12
Real tree → Any, Euclidean, Gluing, If, It, Otherwise, Paris, Start, Such, The, The Paris, They
related to Algebraic groups · 5
Real tree → Bruhat, If, It, SL, Tits
related to Limit of group actions · 5
Real tree → Bestvina, For, Let, Paulin, When
related to Λ-trees · 5
Real tree → If, In, Lambda, The, There
related to Formal definition · 4
Real tree → Gromov, Real, That, This
related to Ultralimits of metric spaces · 2
Real tree → Any, In
is a · 1
Real tree → geodesic metric space which contains no subset homeomorphic to a circle.2
related to Brownian trees · 1
Real tree → Brownian
related to Characterizations · 1
Real tree → Here
related to Examples · 1
Real tree → Real

Important terminology Word statistics

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Important terminology

displaystyle real tree metric trees space spaces points hyperbolic group also mathbb simplicial groups geodesic particular actions -tree arise gromov

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Real treeis ageodesic metric space which contains no subset homeomorphic to a circle.20.90text
Real treerelated to Algebraic groupsIf0.60section
Real treerelated to Algebraic groupsBruhat0.60section
Real treerelated to Algebraic groupsTits0.60section
Real treerelated to Algebraic groupsSL0.60section
Real treerelated to Algebraic groupsIt0.60section
Real treerelated to Brownian treesBrownian0.60section
Real treerelated to CharacterizationsHere0.60section
Real treerelated to ExamplesReal0.60section
Real treerelated to Formal definitionThat0.60section
Real treerelated to Formal definitionThis0.60section
Real treerelated to Formal definitionGromov0.60section

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